Derivative of a Reciprocal
How to find the derivative of a reciprocal 1/g(x): formula (reciprocal rule), 1 example, and its solution.
The derivative of 1/g(x) is -g'(x)/[g(x)]2.
Exampley = 1/(x3 + 2x), y' = ?
1/(x3 + 2x) is the reciprocal of (x3 + 2x).
So y' is equal to ...
Write - and the fraction bar.
Write, the derivative of (x3 + 2x), 3x2 + 2
in the numerator.
Derivative of a Polynomial
Write, the square of (x3 + 2x), (x3 + 2x)2
in the denominator.
y' = -(3x2 + 2)/(x3 + 2x)2
is the derivative of the function.